On the convergence of Bernstein polynomials for some unbounded analytic functions

Tonne, Philip C.

doi:10.1090/s0002-9939-1969-0249641-8

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Cited by 8 publications

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“…Here, motivated from the Voronovskaja formula, our purpose is to obtain a Voronovskaja-type result in the space of bicomplex numbers using bicomplex Bernstein operators mentioned in Section 3. Let us start with the complex Bernstein polynomials for f of order n, which are defined as follows (see [8]): if f :[0,1]→C is a function, n is a positive integer, k = 0, 1, 2, . .…”

Section: Introductionmentioning

confidence: 99%

Some New Results on Bicomplex Bernstein Polynomials

et al. 2021

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The aim of this work is to consider bicomplex Bernstein polynomials attached to analytic functions on a compact C2-disk and to present some approximation properties extending known approximation results for the complex Bernstein polynomials. Furthermore, we obtain and present quantitative estimate inequalities and the Voronovskaja-type result for analytic functions by bicomplex Bernstein polynomials.

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Section: Introductionmentioning

confidence: 99%

Some New Results on Bicomplex Bernstein Polynomials

et al. 2021

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A new generalization of complex Stancu operators

Çetin¹

2019

Math Methods in App Sciences

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In this paper, we investigate approximation properties of the complex form of an extension of the Bernstein polynomials, defined by Stancu by means of a probabilistic method. We obtain quantitative upper estimates for simultaneous approximation and the exact order of approximation by these operators attached to analytic functions in closed disks. Also, we prove that the new generalized complex Stancu operators preserve the univalence, starlikeness, convexity, and spirallikeness in the unit disk.

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Approximation by Bernstein–Faber–Walsh and Szász–Mirakjan–Faber–Walsh Operators in Multiply Connected Compact Sets of ℂ $$\mathbb{C}$$

Gal

2017

Springer Optimization and Its Applications

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On the convergence of Bernstein polynomials for some unbounded analytic functions

Cited by 8 publications

References 1 publication

Some New Results on Bicomplex Bernstein Polynomials

Some New Results on Bicomplex Bernstein Polynomials

A new generalization of complex Stancu operators

Approximation by Bernstein–Faber–Walsh and Szász–Mirakjan–Faber–Walsh Operators in Multiply Connected Compact Sets of ℂ $$\mathbb{C}$$

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